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1 University of Huddersfield Repository Pislaru, Crinela Modelling and Simulation of the Dynamic Behaviour of Wheel-Rail Interface Original Citation Pislaru, Crinela (2012) Modelling and Simulation of the Dynamic Behaviour of Wheel-Rail Interface. In: IET Event: The Railway Wheel-Rail Interface: Damage Mechanisms and Potential Solutions, 5 March 2012, University of Huddersfield. This version is available at The University Repository is a digital collection of the research output of the University, available on Open Access. Copyright and Moral Rights for the items on this site are retained by the individual author and/or other copyright owners. Users may access full items free of charge; copies of full text items generally can be reproduced, displayed or performed and given to third parties in any format or medium for personal research or study, educational or not-for-profit purposes without prior permission or charge, provided: The authors, title and full bibliographic details is credited in any copy; A hyperlink and/or URL is included for the original metadata page; and The content is not changed in any way. For more information, including our policy and submission procedure, please contact the Repository Team at: E.mailbox@hud.ac.uk.

2 Modelling And Simulation Of The Dynamic Behaviour Of Wheel-Rail Interface Dr Crinela Pislaru Diagnostic Engineering Research Centre Contents 2D wheel-rail contact model 3D wheel-rail contact model Dynamic Behaviour of the Wheelset on the Track Conclusions and Future Work

3 Wheel-rail contact forces N represents the Normal Contact Force acting directly on the rail as a result of the axle load, wheelset mass and contact angle. F x represents the longitudinal creep force acting in the rolling direction of the wheel. F y represents the lateral creep force acting in the lateral direction of the wheel. M z represents the spin creep moment caused as a result rotation of the wheel in the vertical z direction due to wheel conicity Normal Contact Problem Normal contact problem involves calculating the normal contact forces acting on the wheel-rail contact. f ( contact angle, axle load of the wheelset, wheelset weight). The calculated normal forces are used to determine the contact patch shape, size and dimension using Hertz Contact Theory. Normal contact forces Contact patch

4 Tangential Contact Problem Tangential contact problem creepages and tangential creep forces developed in the wheel-rail contact as a result of acceleration, braking or traction. Kalker s linear theory lateral, longitudinal and spin creep forces ( for small creepages) For large creepages - Heuristic non-linear model is used to limit the creep forces. Prevents excessive damage to the wheels Reduces probability of derailment Calculated creep forces & lateral, longitudinal and spin creep moments determine total lateral force and spin moment force acting on the wheelset. The lateral and yaw behaviour of the wheelset on the track is investigated by applying Newton s 2 nd law of motion. 2D WHEEL-RAIL CONTACT MODEL Diagnostic Engineering Research Centre

5 Wheel-rail contact models considering contact patch size Hertz Contact Model Non-Hertzian Contact Models Finite Element Method Semi- Hertzian Multi- Hertzian Determination of lateral displacement Wheel-rail contact Geometry Normal Contact Problem Tangential Contact Problem Wheelset Dynamic Behaviour Lateral displacement

6 Wheel-rail contact geometry Wheel profile P1 Rail profile BS113A Wheel-rail contact geometry

7 Wheel rail contact geometry Initial Lateral displacement (y = 0) Derive Lateral and Vertical equations w. r. t ZOY frame Derive Wheel-rail profile equations for Z O Y frame and Z O Y frame u + R φ + ξ φ u φ + η η = 0 y 0 wr z wr rr u + l φ + η φ + u φ + ξ ξ z 0 wr y wr rr δ δ φ rr wr / 2 ξ = (79.37 ( η 3.96) ) rr rr 2 2 1/ 2 ξ = (79.37 ( η ) ) rl r l Solve Simultaneous equations using Quasi-Newton s Method Display Wheel-rail contact coordinates Yes No Is the wheel lateral coordinate greater than the specified limit Save Wheelrail Contact Co-ordinates Stop Wheel rail contact geometry

8 Normal Contact Problem N r cos( δ wr + φ ) + N l cos( δ wl φ ) = (W + mg ) N r sin( δ wr + φ ) N l sin( δ wl φ ) = (W + mg ) φ Normal Contact Problem Relative Curvatures Coefficients 1 1 A = + 2Rwx 2Rwy 1 1 B = + 2R 2 rx Rry Contact patch semi-axis 1/ 3 2 3(1 v ) a = m N 2E( A + B ) 1/ 3 1/ 3 2 3(1 v ) b = n N 2E( A + B ) 1/ 3

9 Normal Contact Problem Tangential Contact Problem Longitudinal creepage Lateral creepage Spin creepage V 1 V + v 1 x = V V 2 V + v 2 y = V Ω v 3 Ω + 3 spin = V

10 Tangential Contact Problem Lateral Creepage (Left/right Wheel-rail contact) v y dy 1 = ψ dt v Longitudinal Creepage l v = x( left) o R l v = x( left) o R λy l + + o dψ R v dt o λy l o dψ R v dt o Left wheel z w x rolling velocity v ψ y Right wheel Spin Creepage dψ λ ϕ = 1 + left v dt R o dψ λ ϕ = 1 right v dt R o x w Tangential Contact Problem Creepages Kalker s Linear Theory Heuristic Non-Linear Model Calculate Creep Forces Fx Fy M = f 11 v x = f 22 v y f 23 v spin z = f 23 v y f 33 v spin Calculate Normalized Creep forces Fx ' = af x F y ' = af y M z ' = am z

11 Parameters for experimental test rig I z Moment of inertial 1.27x10 7 N-mm K py Lateral spring 3.863x10 3 N/mm stiffness K px Longitudinal spin 850 N/mm stiffness C py Lateral damper 8 Ns/mm coefficient C px Longitudinal 100 Ns/mm damper coefficient f 11 Longitudinal linear creep coefficient 8.06x10 6 N f 22 f 23 Lateral linear creep coefficient Lateral/spin linear creep coefficient 8.09x10 6 N 2.2x10 7 N-mm f 33 Spin linear creep 1.27x10 7 N-mm coefficient m Wheelset mass 1250 kg Dynamic behaviour of the Wheelset on the track using Kalker theory

12 Dynamic behaviour of the Wheelset on the track using Heuristic method Diagnostic Engineering Research Centre

13 3D Wheel-rail contact Rigid Contact Method Semi-elastic methods Minimum Distance method Minimum Difference method Global Reference system Local reference frame A = B = (Wheelset centre of mass) (Rail curve length) Auxiliary reference frame

14 Global reference system (O f, X f, Y f, Z f ) defines the track as a three dimensional curve. The Auxiliary reference system (O a, X a, Y a, Z a ) follows the wheelset during program simulation. The local reference system (O w, X w,y w,z w ) is defined whereby Y w is rigidly fixed to the wheelset axle. The origin of the wheelset O w corresponds with the centre of gravity G of the wheelset.

15 P8 Wheel Profile 1:20 BS113A Rail cant Right wheel lateral contact range (692 Y w 815) mm Left wheel lateral contact range (-815 Y w -692) mm

16 Right wheel lateral contact range (700 Y a 780) mm Left wheel lateral contact range (-780 Y a -790) mm

17 Kinematic equation of the contact point in the Auxiliary system w.r.t the local reference frame A 2 = Rotation Matrix (link between Local and Auxiliary Reference System) ψ = yaw angle φ = roll angle u y = Lateral displacement u z = Vertical displacement Find the local minimum between the wheel and the rail contact points C = intersection between the rail surface and line parallel to axis z r D = Take partial derivative of D and reduce to one Dimensional form Check for Indentation

18 Simulated Results Suspended Wheelset Rolling direction Lateral direction Input Parameters Range Step roll angle φ (rad) Yaw angle ψ (rad) Lateral displacement y (mm) 0 10mm 0.5

19 Lateral contact positions on the right wheel Rolling radius difference function

20 Contact angle function Contact patch the wheel-rail at central position a = mm, b = mm

21 Lateral displacement of the wheelset Forward velocity (V = 2.5m/s) Yaw angle function of the wheelset Forward velocity (V = 2.5m/s)

22 Adhesion Detection Creep force estimation 3D Wheel-rail Contact Model Conicity function estimation Wheel profile design and condition monitoring ESTIMATION OF RAILWAY VEHICLE DYNAMIC PARAMETERS USING MOTOR DRIVE BEHAVIOUR Diagnostic Engineering Research Centre

23 Future contributions Technologies for accurate measurement and prediction traction and wheel slip/slide control estimation of vehicle-track dynamics, wear and adhesion system integration for rail wheelset steering and traction control

24 Future contributions Technologies for accurate measurement and prediction measurement of train ground speed with intelligent data processing independent wheel set dynamics parameter identification automated and adaptive model-based prognostics using Monte Carlo simulation, particle filter Future contributions Mechatronic trains of the future remote condition monitoring with wireless intelligent sensors for effective high speed maintenance and inspection of train and track moving-load dynamics

25 Future contributions Mechatronic trains of the future non-linear autonomous systems process monitoring, modelling, control and optimal design expert systems cognitive systems engineering With acknowledged contributions from Professor Andrew Ball Mr Arthur Anyakwo

University of Huddersfield Repository

University of Huddersfield Repository Anyakwo, A., Pislaru, Crinela, Ball, Andrew and Gu, Fengshou Dynamic simulation of a roller rig Original Citation Anyakwo, A., Pislaru, Crinela, Ball, Andrew and Gu,